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  • Please solve RD Sharma class 12 Chapter maxima and minima exercise 17.5 question 2 maths textbook solution.

Please solve RD Sharma class 12 Chapter maxima and minima exercise 17.5 question 2 maths textbook solution.

Answers (1)

x= 32,33

Hint: For maximum or minimum value of z must have \frac{dz}{dx}=0

Given: 64 divide into two parts, sum of cubes of two parts is minimum

Solution: Suppose 64 divide in two parts x and 64 - x then,

z = x^3+(64-x)^3

\frac{dz}{dx}= 3x^2+3(64-x)^2

For maximum and minimum value of z

\frac{dz}{dx}=0

3x^2+3(64-x)^2=0

3x^2=3(64-x)^2

x^2=x^2+4096-128x

x=\frac{4096}{128}

x=32

\frac{d^2z}{dx^2}=6x+6(64-x)

=384>0

\therefore   z is minimum when 64 is divided into two parts 32 and 32

 

 

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